A stochastic model for thermal transport of nanofluid in porous media: Derivation and applications

In this paper, a stochastic thermal transport model is developed for nanofluid flowing through porous media. This model incorporates the influences of nanoparticle migration on convective heat transfer of the colloidal solution. We show that Lévy flight movement patterns of nanoparticles result in the derived model using fractional derivative for the diffusion term. The new thermal transport model is then applied to the mixed convective problem which is solved using finite difference method. Numerical results show that the smaller values of Lévy index γ lead to larger Nusselt numbers, thus the occurrence of long jumps for nanoparticles increases the heat transport of nanofluids. The effects of other involved physical parameters are also presented and discussed.